We consider the nonlinear Schrödinger equation (NLSE) in 1+1 dimension with scalar-scalar self-interaction $\frac{g^2}{\kappa +1}{\left({\psi }^{☆}\psi \right)}^{\kappa +1}$ in the presence of the external forcing terms of the form $r{e}^{-i(kx+\theta )}-\delta \psi$. We find new exact solutions for this problem and show that the solitary wave momentum is conserved in a moving frame where $v_k=2k$. These new exact solutions reduce to the constant phase solutions of the unforced problem when $r\to 0.$ In particular we study the behavior of solitary wave solutions in the presence of these external forces in a variational approximation which allows the position, momentum, width, and phase of these waves to vary in time. We show that the stationary solutions of the variational equations include a solution close to the exact one and we study small oscillations around all the stationary solutions. We postulate that the dynamical condition for instability is that $dp\left(t\right)/d\dot{q}\left(t\right)<0$, where $p\left(t\right)$ is the normalized canonical momentum $p\left(t\right)=\frac{1}{M\left(t\right)}\frac{\partial L}{\partial \dot{q}}$, and $\dot{q}\left(t\right)$ is the solitary wave velocity. Here $M\left(t\right)=\int dx{\psi }^{☆}(x,t)\psi (x,t)$. Stability is also studied using a “phase portrait” of the soliton, where its dynamics is represented by two-dimensional projections of its trajectory in the four-dimensional space of collective coordinates. The criterion for stability of a soliton is that its trajectory is a closed single curve with a positive sense of rotation around a fixed point. We investigate the accuracy of our variational approximation and these criteria using numerical simulations of the NLSE. We find that our criteria work quite well when the magnitude of the forcing term is small compared to the amplitude of the unforced solitary wave. In this regime the variational approximation captures quite well the behavior of the solitary wave.

The dynamic range measures the capacity of a system to discriminate the intensity of an external stimulus. Such an ability is fundamental for living beings to survive: to leverage resources and to avoid danger. Consequently, the larger is the dynamic range, the greater is the probability of survival. We investigate how the integration of different input signals affects the dynamic range, and in general the collective behavior of a network of excitable units. By means of numerical simulations and a mean-field approach, we explore the nonequilibrium phase transition in the presence of integration. We show that the firing rate in random and scale-free networks undergoes a discontinuous phase transition depending on both the integration time and the density of integrator units. Moreover, in the presence of external stimuli, we find that a system of excitable integrator units operating in a bistable regime largely enhances its dynamic range.

We provide an extension of a recent approach to study nonequilibrium thermodynamics [Gujrati, Phys. Rev. E 81, 051130 (2010), to be denoted by I in this work] to inhomogeneous systems by considering the latter to be composed of quasi-independent subsystems. The system $\Sigma$ along with the (macroscopically extremely large) medium $\tilde{\Sigma }$ form an isolated system ${\Sigma }_0$. The fields (temperature, pressure, etc.) of $\Sigma$ and $\tilde{\Sigma }$ differ unless at equilibrium. We show that the additivity of entropy requires quasi-independence of the subsystems, which results from the interaction energies between different subsystems being negligible so the energy also becomes additive. The thermodynamic potentials such as the Gibbs free energy that continuously decrease during approach to equilibrium are determined by the fields of the medium and exist no matter how far the subsystems are out of equilibrium, so their fields may not even exist. This and the requirement of quasi-independence make our approach differ from the conventional approach used by de Groot and others, as discussed in the text. We find it useful to introduce the time-dependent Gibbs statistical entropy for ${\Sigma }_0$, from which we derive the Gibbs entropy of $\Sigma$; in equilibrium this entropy reduces to the equilibrium thermodynamic entropy. As the energy depends on the frame of reference, the thermodynamic potentials and the Gibbs fundamental relation, but not the entropy, depend on the frame of reference. The possibility of relative motion between subsystems described by their net linear and angular momenta gives rise to viscous dissipation. The concept of internal equilibrium introduced in I is developed further here and its important consequences are discussed for inhomogeneous systems. The concept of internal variables (various examples are given in the text) as variables that cannot be controlled by the observer for nonequilibrium evolution is also discussed. They are important because the concept of internal equilibrium in the presence of internal variables no longer holds if internal variables are not used. The Gibbs fundamental relation, thermodynamic potentials, and irreversible entropy generation are expressed in terms of observables and internal variables. We use these relations to eventually formulate the nonequilibrium thermodynamics of inhomogeneous systems. We also briefly discuss the case when bodies form an isolated system without any medium to obtain their irreversible contributions and show that this case does not differ from when bodies are in an extremely large medium.

We follow the consequences of internal equilibrium in nonequilibrium systems that has been introduced recently [Gujrati, Phys. Rev. E 81, 051130 (2010) and Gujrati, Phys. Rev. E 85, 041128 (2012).] to obtain the generalization of the Maxwell relation and the Clausius-Clapeyron relation that are normally given for equilibrium systems. The use of Jacobians allows for a more compact way to address the generalized Maxwell relations in the presence of internal variables. The Clausius-Clapeyron relation in the subspace of observables shows not only the nonequilibrium modification but also the modification due to internal variables that play a dominant role in glasses to which we apply the above relations. Real systems do not directly turn into glasses (GL) that are frozen structures from the supercooled liquid state L; there is an intermediate state (gL) where the internal variables are not frozen. A system possesses several kinds of glass transitions, some conventional (L$\to$gL; gL$\to$GL) in which the state changes continuously and the transition mimics a continuous or second-order transition, and some apparent (L$\to$gL; L$\to$GL) in which the free energies are discontinuous so that the transition appears as a zeroth-order transition, as discussed in the text. We evaluate the Prigogine-Defay ratio $\Pi$ in the subspace of the observables at these transitions. We find that it is normally different from $1,$ except at the conventional transition L$\to$gL, where $\Pi =1$.

This paper studies a periodic driven diffusive system, which separates into two equal-sized parts with different values of hopping rates. Competition of the two different driven parts leads to various bulk-driven phase transitions, including shock and antishock. More interestingly, for the symmetric scenario, one can observe shock and antishock simultaneously in the system. We have explained the coexistence of shock and antishock via the effective boundary reservoir density. Theoretical analysis has been carried out to characterize the emerging nonequilibrium steady states, which is in good agreement with Monte Carlo simulations.

This paper has studied spontaneous symmetry breaking (SSB) phenomenon in two types of two-channel asymmetric simple exclusion processes (ASEPs). One common feature of the two systems is that interactions for each species of particle happen at only one site, and the system reduces to two independent ASEPs when interaction vanishes. It is shown that with the weakening of interaction, the SSB is suppressed. More interestingly, the SSB disappears before the interaction is eliminated. Our work thus indicates that local interaction has to be strong enough to produce SSB. The mean-field analysis has been carried out, and the results are consistent with the simulation ones.

Nonequilibrium steady states of Markov processes give rise to nontrivial cyclic probability fluxes. Cycle decompositions of the steady state offer an effective description of such fluxes. Here we present an iterative cycle decomposition exhibiting a natural dynamics on the space of cycles that satisfies detailed balance. Expectation values of observables can be expressed as cycle “averages,” resembling the cycle representation of expectation values in dynamical systems. We illustrate our approach in terms of an analogy to a simple model of mass transit dynamics. Symmetries are reflected in our approach by a reduction of the minimal number of cycles needed in the decomposition. These features are demonstrated by discussing a variant of an asymmetric exclusion process. Intriguingly, a continuous change of dominant flow paths in the network results in a change of the structure of cycles as well as in discontinuous jumps in cycle weights.

Diffusive transport is characterized by the scaling law ${\left(\text{length}\right)}^2\propto \left(\text{time}\right)$. In this paper we show that this relationship is significantly altered in curved analog spacetimes. This circumstance provides an opportunity to tailor diffusion: by a suitable design of the analog metric, it is possible to create materials where diffusion is either faster or slower than in normal media, as desired. This prediction can, in principle, be tested experimentally with optical analogs, curved graphene sheets, and so on (indeed with any analog spacetime).

The concept of local accumulation time (LAT) was introduced by Berezhkovskii and co-workers to give a finite measure of the time required for the transient solution of a reaction-diffusion equation to approach the steady-state solution [A. M. Berezhkovskii, C. Sample, and S. Y. Shvartsman, Biophys. J. 99, L59 (2010); A. M. Berezhkovskii, C. Sample, and S. Y. Shvartsman, Phys. Rev. E 83, 051906 (2011)]. Such a measure is referred to as a critical time. Here, we show that LAT is, in fact, identical to the concept of mean action time (MAT) that was first introduced by McNabb [A. McNabb and G. C. Wake, IMA J. Appl. Math. 47, 193 (1991)]. Although McNabb's initial argument was motivated by considering the mean particle lifetime (MPLT) for a linear death process, he applied the ideas to study diffusion. We extend the work of these authors by deriving expressions for the MAT for a general one-dimensional linear advection-diffusion-reaction problem. Using a combination of continuum and discrete approaches, we show that MAT and MPLT are equivalent for certain uniform-to-uniform transitions; these results provide a practical interpretation for MAT by directly linking the stochastic microscopic processes to a meaningful macroscopic time scale. We find that for more general transitions, the equivalence between MAT and MPLT does not hold. Unlike other critical time definitions, we show that it is possible to evaluate the MAT without solving the underlying partial differential equation (pde). This makes MAT a simple and attractive quantity for practical situations. Finally, our work explores the accuracy of certain approximations derived using MAT, showing that useful approximations for nonlinear kinetic processes can be obtained, again without treating the governing pde directly.

The ferrofluid emulsion, made of kerosene-based ferrofluid droplets suspended in nonmiscible aviation oil, demonstrates experimentally the nonmonotonic dependence of the effective magnetic permeability as a function of the uniform static magnetic field. In weak fields the emulsion permeability rapidly grows; it reaches its maximum at fields on the order of 1 kA/m; after that, it decays to zero. The theoretical explanation of the effect, as we show here, could be based on the following idea: In a weak magnetic field the growth of the induced droplet magnetic moment is faster than the linear one due to the droplet elongation accompanied by the reduction of the demagnetizing field. Further increase of the external magnetic field strength cannot lead to a significant decrease of the demagnetizing field, as the droplets are already highly elongated. On the other hand, the magnetic susceptibility of the ferrofluid reduces with the field strength. Thus, the effective magnetic permeability of the ferrofluid suspension starts decreasing. The developed theoretical model describes well the experimental observations.

Our investigation of endothelial cell rheology using optical magnetic twisting cytometry revealed that with time following incubation of ferromagnetic beads on the cells, beads were sinking into the cells and an increasing number of beads demonstrated apparent absurd negative rheological properties. In parallel, the beads’ average rheological response changed considerably over time, both in magnitude and in distribution. It was hypothesized that the apparent negative rheological response was related to the above sinking process of seeded beads into the cells, resulting in an elevation of the beads’ rotation axis, thus causing a reversal of the beads’ lateral movement direction in response to twisting external magnetic excitation. The results suggest that microbead-based rheological characterization of cells should be interpreted with caution, while considering the time of data acquisition.

The importance of post-transcriptional regulation by microRNAs (miRNAs) has recently been recognized in almost all cellular processes. When participating in cellular processes, miRNAs mainly mediate mRNA degradation or translational repression. Recently computational and experimental studies have identified an abundance of motifs involving miRNAs and transcriptional factors (TFs). The simplest motif is a two-node miRNA-mediated feedback loop (MFL) in which a TF regulates an miRNA and the TF itself is negatively regulated by the miRNA. In this paper we present a general computational model for the MFL based on biochemical regulations and explore its dynamics by using bifurcation analysis. Our results show that the MFL can behave either as switches or as oscillators, depending on the TF as a repressor or an activator. These functional features are consistent with the widespread appearance of miRNAs in fate decisions such as proliferation, differentiation, and apoptosis during development. We found that under the interplay of a TF and an miRNA, the MFL model can behave as switches for wide ranges of parameters even without cooperative binding of the TF. In addition, oscillations induced by the miRNA in the MFL model require neither an additional positive feedback loop, nor self-activation of the gene, nor cooperative binding of the TF, nor saturated degradation. Therefore, the MFL may provide a general network structure to induce bistability or oscillations. It is hoped that the results presented here will provide a new view on how gene expression is regulated by miRNAs and further guidance for experiments. Moreover, the insight gained from this study is also expected to provide a basis for the investigation of more complex networks assembled by simple building blocks.

Despite research spanning several decades, the exact value of the shear modulus $G_s$ of the erythrocyte membrane is still ambiguous, and a wealth of studies, using measurements based on micropipette aspirations, ektacytometry systems and other flow chambers, and optical tweezers, as well as application of several models, have found different average values in the range 2–$10\mu$N/m. Our study shows that different methodologies have predicted the correct shear modulus for the specific membrane modeling employed, i.e., the variation in the shear modulus determination results from the specific membrane modeling. Available experimental findings from ektacytometry systems and optical tweezers suggest that the dynamics of the erythrocyte membrane is strain hardening at both moderate and large deformations. Thus the erythrocyte shear modulus cannot be determined accurately using strain-softening models (such as the neo-Hookean and Evans laws) or strain-softening/strain-hardening models (such as the Yeoh law), which overestimate the erythrocyte shear modulus. According to our analysis, the only available strain-hardening constitutive law, the Skalak et al. law, is able to match well both deformation-shear rate data from ektacytometry and force-extension data from optical tweezers at moderate and large strains, using an average value of the shear modulus of $G_s=2.4$–$2.75\mu$N/m, i.e., very close to that found in the linear regime of deformations via force-extension data from optical tweezers, $G_s=2.5\pm 0.4\mu$N/m. In addition, our analysis suggests that a standard deviation in $G_s$ of $0.4$–$0.5\mu$N/m (owing to the inherent differences between erythrocytes within a large population) describes well the findings from optical tweezers at small and large strains as well as from micropipette aspirations.

We theoretically show that completely stochastic fast physical random bit generation at a rate of more than one gigabit per second can be realized by using lasers with optical delayed feedback which creates high-dimensional chaos of laser light outputs. The theory is based on the mixing property of chaos, which transduces microscopic quantum noise of spontaneous emission in lasers into random transitions between discrete macroscopic states.

The formation of cold dense structures in a hydrogen isotope plasma, caused by the penetration of impurities from a localized source, is modelled numerically. It is shown that a bubble structure with very high densities and low temperatures of all plasma components, i.e. electrons, main and impurity ions, arises if the density of impurity neutrals in the source exceeds a critical level. The major cause of this condensation phenomenon are Coulomb collisions between main and impurity ion species which, on the one hand, cool down the main ions and, on the other hand, confine impurity ions near the source. This mechanism is efficient even if the impurity radiation, considered usually as the most important cause of condensation instabilities, is completely switched off in the calculations. On the contrary, without ion-ion Coulomb collisions the radiation losses result only in a transient cooling of electrons with a later recovery of their temperature to a level comparable with the initial one.

The macroscopic electromagnetic force on dielectric bodies and the related problem of the momentum conservation are discussed. It is argued that different forms of the momentum conservation and, respectively, different forms of the force density, correspond to the different ordering in the macroscopic averaging procedure. Different averaging procedures and averaging length scale assumptions result in expressions for the force density with vastly different force density profiles which can potentially be detected experimentally by measuring the profiles of the internal stresses in the medium. The expressions for the Helmholtz force is generalized for the dissipative case. It is shown that the net (integrated) force on the body in vacuum is the same for Lorentz and Helmholtz expressions in all configuration. The case of a semi-infinite medium is analyzed and it is shown that explicit assumptions on the boundary conditions at infinity remove ambiguity in the force on the semi-infinite dielectric.

We analyze the appropriate form for the generalized Stokes-Einstein relation (GSER) for viscoelastic solids and fluids when bead inertia and medium inertia are taken into account, which we call the inertial GSER. It was previously shown for Maxwell fluids that the Basset (or Boussinesq) force arising from medium inertia can act purely dissipatively at high frequencies, where elasticity of the medium is dominant. In order to elucidate the cause of this counterintuitive result, we consider Brownian motion in a purely elastic solid where ordinary Stokes-type dissipation is not possible. The fluctuation-dissipation theorem requires the presence of a dissipative mechanism for the particle to experience fluctuating Brownian forces in a purely elastic solid. We show that the mechanism for such dissipation arises from the radiation of elastic waves toward the system boundaries. The frictional force associated with this mechanism is the Basset force, and it exists only when medium inertia is taken into consideration in the analysis of such a system. We consider first a one-dimensional harmonic lattice where all terms in the generalized Langevin equation—i.e., the elastic term, the memory kernel, and Brownian forces—can be found analytically from projection-operator methods. We show that the dissipation is purely from radiation of elastic waves. A similar analysis is made on a particle in a continuum, three-dimensional purely elastic solid, where the memory kernel is determined from continuum mechanics. Again, dissipation arises only from radiation of elastic shear waves toward infinite boundaries when medium inertia is taken into account. If the medium is a viscoelastic solid, Stokes-type dissipation is possible in addition to radiational dissipation so that the wave decays at the penetration depth. Inertial motion of the bead couples with the elasticity of the viscoelastic material, resulting in a possible resonant oscillation of the mean-square displacement (MSD) of the bead. On the other hand, medium inertia (the Basset force) tends to attenuate the oscillations by the dissipation mechanism described above. Thus competition between bead inertia and medium inertia determines whether or not the MSD oscillates. We find that, if the medium density is larger than $4/7$ of the bead density, the Basset damping will suppress oscillations in the MSD; this criterion is sufficient but not necessary to present oscillations.

We introduce a model for random-walking agents on a two-dimensional periodic lattice, where the dynamic interaction network is defined using local short-range interactions and $E$ randomly added long-range interactions. With periodic states for agents and an interaction rule of repeated averaging, we numerically find two types of metastable states at low- and high-$E$ limits, respectively, along with consensus states. If we apply this model to opinion dynamics, metastable states can be interpreted as sustainable diversities in our societies, and our results then imply that, while diversities decrease and eventually disappear with more long-range interactions, other types of diverse states can appear under this rule when networks are almost fully connected.

We study the well-known multiplicative log-normal cascade process in which the multiplication of Gaussian and log normally distributed random variables yields time series with intermittent bursts of activity. Due to the nonstationarity of this process and the combinatorial nature of such a formalism, its parameters have been estimated mostly by fitting the numerical approximation of the associated non-Gaussian probability density function to empirical data, cf. Castaing et al. [Physica D 46, 177 (1990)]. More recently, alternative estimators based upon various moments have been proposed by Beck [Physica D 193, 195 (2004)] and Kiyono et al. [Phys. Rev. E 76, 041113 (2007)]. In this paper, we pursue this moment-based approach further and develop a more rigorous generalized method of moments (GMM) estimation procedure to cope with the documented difficulties of previous methodologies. We show that even under uncertainty about the actual number of cascade steps, our methodology yields very reliable results for the estimated intermittency parameter. Employing the Levinson-Durbin algorithm for best linear forecasts, we also show that estimated parameters can be used for forecasting the evolution of the turbulent flow. We compare forecasting results from the GMM and Kiyono et al.'s procedure via Monte Carlo simulations. We finally test the applicability of our approach by estimating the intermittency parameter and forecasting of volatility for a sample of financial data from stock and foreign exchange markets.